Continuous time capacitor-tuner integrator

ABSTRACT

A tunable integrator circuit having a main amplifier with an input resistor R and a feedback capacitor C and a tuning amplifier having a variable gain k between the output of the main amplifier and the feedback capacitor. The circuit has an effective capacitance of kC. Thus the integrator can be tuned to compensate for temperature and processing variations of the RC product by adjusting the gain of the tuning amplifier. The tuning amplifier can also be used to multiply the effective capacitance of the filter, kC, by increasing the gain k of the tuning amplifier beyond that needed to compensate for RC variations, thus reducing the area required for on-chip capacitances while maintaining a constant resistance. The circuit can be used independently or in conjunction with a capacitor array.

TECHNICAL FIELD

This invention is related to an article comprising a continuous timecapacitor-tuner integrator. More particularly, this invention relates toa continuous time capacitor-tuner integrator used to adjust thecapacitance and thus the RC product of a continuous time filter.

BACKGROUND OF THE INVENTION

Continuous-time filters have become widely used in commercialapplications. Currently, this area is dominated bytransconductor-capacitor (gm-C) filters. However, in low and mediumfrequency applications the active RC filters feature higher dynamicrange and lower distortion. Active RC filters are constructed fromresistors, capacitors, and integrated amplifiers. A basic building blockis an integrator comprising an op-amp with an input resistor and afeedback capacitor. For low to medium frequency applications, theamplifiers can be treated as having essentially infinite gain and inputimpedance. Because little or no current is drawn by the amplifiers, theamplifier inputs function as virtual grounds and substantially all ofthe input signal is applied to the resistors and capacitors. Thus, theoperating characteristics of the filter are determined by the various RCproducts.

In some situations, it has proven useful to provide a feedback amplifierin series with a compensating feedback capacitor. For example, a unitygain amplifier placed in the feedback path has been used to improvestability of MOS amplifier circuits. Y. P. Tsividis, "Single-Channel MOSAnalog IC's," IEEE Journal of Solid-State Circuits, Vol. SC-13, No. 3,pp. 389-90, June 1978. A non-tunable amplifier with gain less than orequal to 1 has also been used in phase-lead integrators to cancel out"errors" in the quality factor. Q. K. Martin and A. S. Sedra, "On theStability of the Phase-Lead Integrator," IEEE Trans. Circuits Syst.,Vol. CAS-24, pp. 321-324, June 1977. According to theory, making theunity-gain bandwidth of the main and feedback amplifiers identicalresults in a value of Q which approaches infinity. Thus, attempts toimprove Q in this manner used matched circuits for the main and feedbackamplifiers. In practice, however, non-ideal aspects of the circuitscause the integrator to oscillate.

Another drawback to using active integrated RC filters is the variationof the RC product of up to +/-50% from its nominal value due to processand temperature variations. Tuning of the frequency response of thefilter to compensate for this variation remains the main problem in VLSIimplementation. Although, as discussed above, feedback amplifiers havebeen used to improve performance, they have not been used to achieve atunable filter. Instead, there are three conventional approaches toimplementing monolithic active RC filters: MOSFET-C, R-MOSFET-C, and R-CArray. In MOSFET-C filters, the resistors are replaced by MOSFETSdevices that can be tuned via gate terminals. The R-MOSFET-C approachimproves linearity of the MOSFET-C technique by inserting resistors inseries with the MOSFETS. However, this technique also degrades the noiseperformance of the filter. The third approach, R-C Array, achieves thehighest dynamic range reported so far by using resistors and replacingcapacitors with capacitor arrays which are tuned with a digital signalwhose value is set during an initial tuning cycle. A filter usingcapacitor arrays is especially useful in low-noise high-linearityapplications.

However, the major disadvantage with the capacitor array approach isthat the capacitor arrays require significant area. This is becomingmore important with advances in silicon technology. As the active areasof the transistors decrease, the area required to fabricate the activecircuits such as amplifiers and bias circuits shrink. However, there hasbeen little improvement in on-chip capacitor density. As a result, thearea of continuous time filters is increasingly dominated by thecapacitance size. Another disadvantage of the capacitor array approachis that a filter utilizing capacitor arrays cannot operate while it isbeing tuned.

SUMMARY OF THE INVENTION

According to the present invention, an analog tuned capacitor integratoris provided which comprises an integrator having a tuning amplifier withvariable gain k connected to the output of a main amplifier and drivinga capacitor, with capacitance C, connected to an input of the mainamplifier. This creates a feedback path with an effective capacitance ofkC. An input resistor with resistance R is also connected to the inputof the main amplifier. Since the filtering characteristics of theintegrator are determined by the RC product of the circuit, here equalto kRC, the effective capacitance, and thus frequency response of thefilter, is tuned by changing the gain of the tuning amplifier. Ascompared to the R-C array approach, this technique offers area savingswith a marginal increase in noise. Process variations of the RC productsof +/-50% can be easily accommodated by changing the gain k in the rangeof 0.5 to 1.5. This configuration can also be used to multiply theeffective capacitance of the filter, kC, by increasing the gain k of thetuning amplifier beyond that needed to compensate for RC variations,thus allowing substantially smaller physical capacitors to be used inthe circuit. This reduces the area required for on-chip capacitanceswhile maintaining a constant resistance. This is especially useful inlow frequency applications where the capacitances are typically large.

According to the present invention, and contrary to the prior art, thetuning amplifier is not configured as a unity gain amplifier, nor is itdesigned to be identical to the main amplifier or have the samebandwidth. Instead, the main and feedback amplifiers are different fromone another, and in particular, the tuning amplifier has a greaterbandwidth than the main amplifier. The circuit remains stable, even as kis varied, so long as bandwidth of the tuning amplifier is greater thanthat of the main amplifier. This is not a major design limitationbecause the tuning amplifier drives only a capacitive load and its owninternal resistances. Thus, it can have a simpler design than the mainamplifier, and therefore will typically have a greater bandwidth andhigher unity gain frequency.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features of the present invention will be morereadily apparent from the following detailed description and drawings ofillustrative embodiments of the invention in which:

FIG. 1 is a schematic diagram of one embodiment of a capacitor-tunerintegrator according to the present invention;

FIG. 2 is a schematic diagram of a Tow-Thomas biquad amplifier which istunable according to the present invention;

FIG. 3a is a schematic diagram of the circuit of FIG. 1 showing oneembodiment of a variable-gain tuning amplifier;

FIG. 3b is the circuit of FIG. 3a with an electronically tunable tuningamplifier;

FIG. 4 is a schematic diagram of a one embodiment of a differentialvariable-gain tuning amplifier to be used in the present invention;

FIG. 5 is a schematic diagram of a hybrid circuit combining the presetinvention with a capacitor array;

FIG. 6a is a graph of the open-loop gain A and the inverse of thefeedback factor β of a conventional integrator with a single-poleop-amp;

FIG. 6b is a graph of A versus 1/β for an integrator with a unity gainfeedback amplifier, where the feedback and the main amplifiers areidentical single-pole op-amps;

FIG. 6c is a graph of A versus 1/β with where the gain of the feedbackamplifier is increased and where the feedback and the main amplifiersare identical single-pole op-amps;

FIG. 7a is a graph of A versus 1/β of a conventional integrator with atwo-pole op-amp;

FIG. 7b is a graph of A versus 1/β for an integrator with a unity gainfeedback amplifier, where the feedback and the main amplifiers areidentical two-pole op-amps; and

FIG. 7c is a graph of A versus 1/β for a non-inverting integrator ofFIG. 3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

FIG. 1 is a schematic diagram of one embodiment of a capacitor-tunerintegrator 10 according to the present invention which comprises a mainamplifier 20 having an input resistor 22 (also referred to as RO)connecting V_(in) to inverting input 23 and a feedback loop comprising atuning amplifier 26 which is driven by the output V_(out) 21 of the mainamplifier 20 and a capacitor 24 having capacitance C and connectedbetween the output of the tuning amplifier 26 and an input 23 of themain amplifier 20. The ideal operation of the tunable integrator isdescribed by: ##EQU1## where k is the gain of the tuning amplifier 26.The value of the effective capacitance in the filter, kC, can be tunedby changing k. Process variations of +/-50% in the RC product can beeasily accommodated by providing a tuning amplifier with a variable gainin the range of 0.5 to 1.5.

This configuration can also advantageously be used to provide a tunablecapacitor multiply. The effective capacitance of the filter, kC, isincreased by increasing the gain k of the tuning amplifier beyond thatneed to compensate for RC product variations. This allows substantiallysmaller physical capacitors to be used in the circuit, thus reducing thearea required for on-chip capacitances while maintaining a constantinput resistance. For low frequency applications, this is especiallyuseful since low frequency filters typically require a capacitance whichis too large to economically integrate on a chip, e.g., on the order of1000 pf. According to the present invention, a tuning amplifier with again of 5, for example, gives an effective capacitance of 1000 pf with aphysical capacitor of only 200 pf, small enough to be integrated onto achip.

It should be noted that the multiplication factor is limited due tostability and output swing requirements. Stability is discussed below.The output swing requirements present an upper limit for themultiplication factor. In the filter optimized for maximum dynamicrange, the gain is essentially shifted to the first stage, and theoutputs of different stages are designed to peak at the same level.Because of this, the multiplication factor is determined by the filteroutput swing requirement and the available output swing of the tuningamplifier. However, the situation is different in low distortionfilters, where some gain distribution is necessary to avoid clipping inthe presence of strong interferers. Here, each stage should be assignedits own multiplication factor so that the tuning amplifiers will not beclipped.

The capacitor-tuner integrator 10 shown in FIG. 1 can be easily adaptedto more complex amplifier circuits. For example, FIG. 2 is a schematicdiagram of a Tow-Thomas biquad amplifier 50 which is tunable accordingto the present invention. The amplifier 50 comprises op-amps 52 and 54,resistors 56-70 and feedback capacitors 72, 74, 76 and 78. As shown, thefeedback capacitors 72 and 74 are tuned by tuning amplifier 80 which isconnected to the output of op-amp 52. Similarly, feedback capacitors 76and 78 are tuned by tuning amplifier 82 connected to the output ofop-amp 54.

As shown in FIGS. 1 and 2, the main amplifier(s) must drive resistiveloads. Thus, a two stage amplifier or buffered single stage amplifier istypically required. In contrast, a tuning amplifier drives only acapacitive load (and its internal resistance) and can therefore be madesimpler than the main amplifier, i.e. single stage. As a result, it isrelatively easy to design the tuning amplifier with a higher bandwidththan the main amplifier so that the circuit is stable, as discussedbelow. As will be recognized by those skilled in the art, when designinga low-pass filter, the input stage of the tuning amplifier can beconsiderably smaller than the main amplifier. This is because thecontribution of the 1/f noise from the tuning amplifier is attenuated bythe capacitance in series with it. Because of the small size of theinput stage, the input capacitance of the amplifier can be small,further increasing stability of the integrator.

There are various ways in which the tuning amplifier 26 may beconfigured. One arrangement for the circuit of FIG. 1 is shown in FIG.3a. The tuning amplifier 26 comprises an op-amp 90 having a variablefeedback resistance 92 (R₁) and a variable input resistance 94 (R₂). Thegain k of the tuning amplifier 26 is therefore R₁ /R₂ and can be variedby adjusting the resistance of either or both of resistors R₁ and R₂.

There are many ways to implement resistors R₁ and R₂ so that theirresistance can be varied to tune the filter, as will be apparent tothose of skill in the art. The gain of the tuning amplifier 26 can beelectronically controlled by forming one or both of the tuning resistorsfrom active components such as MOS transistors 92', 94', as shown inFIG. 3b, and varying the bias voltages V_(ref1) and V_(ref2). Thedesired gate voltages V_(ref1), and V_(ref2) can be set by any number ofconventional techniques. For example, using conventional feedbacktechniques, the gate voltage applied a MOS resistor can be adjusted sothat the resistance of the MOS device equals the resistance of a knownreference resistor. Alternatively, the resistors can be tuned directlyby the user if non-integrated devices, such as potentiometers, are used.

In a preferred embodiment, only resistor R₁ is variable. In a morepreferred embodiment, the circuit is integrated, R₁ is variable, andresistors R₀ and R₂ are formed from the same material and during thesame process. In this situation, resistors R₀ and R₂ will be subject tothe same process and temperature variations and the relative effect ofthese variations will cancel out. Thus, resistor R₂ can be defined ashaving resistance αR₀, where α is a constant. The gain of the tuningamplifier 26 is then k=R₁ /αR₀. Substituting into Equation 1, above,results in: ##EQU2## Thus, the effective capacitance of the filter canbe varied by adjusting the resistance of R₁.

It is advantageous that the tuning amplifier 26 have a linear responseto minimize signal distortions in the filter. In a preferredarrangement, a highly linear and highly tunable amplifier 26 is providedby using Moon's multiplier technique as described by U. K. Moon and B.S. Song in "Design of a Low-Distortion 22-KHz Fifth-Order BesselFilter," IEEE J. Solid-State Circuits, Vol. 28, pp. 1254-1263, December1993. A differential tuning amplifier 26 configured using a modifiedversion of Moon's technique is illustrated in FIG. 4. The circuit hasinput resistors 94, 94' connected to op-amp 100. Resistors 94, 94'correspond to a non-variable version of resistor R₂ in FIG. 3a,discussed above. The output of the op-amp 100 drives a cross-connectedfeedback loop comprising resistors 110, 112 and MOS transistors 102,104, 106, and 108. The impedances of the MOS transistors 102-108, andthus the gain of the tuning amplifier, is set by a reference voltage,V_(ref).

Those skilled in the art will recognize that other configurations forthe tuning amplifier 26 may also be used in accordance with variousdesign considerations. For example, when low voltage supplies are used,a closed-loop op-amp configuration may be undesirable. Instead, thetuning amplifier 26 may be an open-loop amplifier comprising adifferential input stage (and a buffer stage if needed) can be used. Thegain is controlled by adjusting the biasing of one or more transistorsin the amplifier. Because open-loop amplifiers do not require switchesor gate-controlled devices, they can operate at lower voltages thanclosed-loop amplifiers. Further, they generally consume less power andhave a larger bandwidth than an op-amp based tuning amplifier discussedabove. A drawback, however, is that open-loop amplifiers trade linearityfor more convenient tuning.

A hybrid embodiment combining the preset invention with a capacitorarray is shown in FIG. 5. In this embodiment, the feedback capacitor 24of FIG. 1 is replaced with a capacitor array 120. This arrangement has atuning amplifier 26 which does not need to compensate for the full+/-50% variation in the RC product. Instead, the gain of the tuningamplifier 26 is adjusted to compensate for the process variations of theresistances. Then, the capacitor arrays are set to accommodate forprocess variations in the capacitor. Since the capacitor processvariations are typically small, with some processes achieving atolerance of less than +/-10%, the capacitor arrays can also be muchsmaller than those used in conventional R-C Array filters which must belarge enough to be tuned to compensate for variations in both R and C.Furthermore, since the capacitance of the array varies only slightlywith variations in temperature, the array itself will generally onlyneed to be tuned once. After the capacitor array 120 is tuned, filtertuning to compensate for variations in resistance due to process and/ortemperature may be automatically performed with or without a drivingsignal V_(in) present in the filter. In contrast, on-line tuning is notpossible while calibrating a capacitor array in an R-C Array filter. Thehybrid integrator as discussed here may also be used to formprogrammable filters by using large capacitor arrays that can beprogrammed to obtain different frequency responses in a single filter.

Regardless of which embodiment is selected for the tuning amplifier 26and the method of adjusting its gain to tune the filter 10, the presenceof two amplifiers in a series feedback loop makes it necessary toconsider stability of the circuit when designing the tuning amplifier26. The first order stability analysis of the capacitor-tuner integrator10 is very similar to the stability analysis of a phase-lead integrator.See, e.g, K. Martin and A. S. Sedra, "On the Stability of the Phase-LeadIntegrator," IEEE Trans. Circuits Syst., Vol. CAS-24, pp. 321-324, June,1977. However, the stability analysis for the capacitor tuner integratorof the present invention is more general. One reason for this is thegain of the tuning amplifier 26 is variable, ranging, in one embodiment,from about 0.5 to 1.5 to compensate for RC process variations. Incontrast, a phase-lead integrator requires a constant feedback amplifiergain of less than or equal to 1. Another reason is that the presentinvention may be used as a tunable capacitor multiplier to increase theeffective RC constant, and therefore the gain of the tuning amplifiermay be higher than 1.5, i.e., the amplifier gain may be tunable by about+/-50% percent around a center value greater than 1. Becausemathematical analysis, such as is discussed by Martin and Sedra, isoften not very insightful and becomes complicated when a higher-ordersystem is analyzed, stability of the capacitor-tuner/multiplierintegrator according to the present invention is discussed herein usinggraphical techniques, and with reference to the graphs in FIGS. 6 and 7.

FIG. 6a is a graph of the open-loop gain A and the inverse of thefeedback factor β of a conventional integrator with a single-pole op-ampwhere f_(t) is the unity gain frequency of the main amplifier (where Acrosses the x-axis) and f_(c) is the point where the 1/β and A curvescross. This configuration is stable because the rate of closure is about20 dB/dec, i.e., the phase margin is about 90 degrees at the unity gainfrequency, f_(t). FIG. 6b is a graph of A versus 1/β for an integratorwith a unity gain feedback amplifier, where the feedback and the mainamplifiers are identical single-pole op-amps, such as in conventionalphase-lead integrators. In theory, the phase margin at f_(t) (alsof_(c)) is 45 degrees and the circuit is stable. However, the circuit ison the verge of instability and any increase in the gain of the feedbackamplifier may create an unstable circuit. FIG. 6c is a graph of A versus1/B where the gain of the feedback amplifier is increased and where thefeedback and the main amplifiers are identical single-pole op-amps.Increasing the gain of the feedback amplifier lowers its 3 dB frequency.As a result, the feedback factor 1/β will be greater than one before theopen-loop gain crosses the x-axis, as shown. The phase margin at f_(c)is about 0 degrees and the integrator is unstable. Accordingly, thecircuit of the present invention is stable when the bandwidth of thetuning amplifier 26 is greater than that of the main amplifier 20. Inother words, the phase margin at f_(c), where A and 1/β cross, should begreater than zero.

Practical op-amps are described better by two-pole models. FIG. 7a showsan open-loop gain vs. the inverse feedback of a conventional integratorwith a two-pole op-amp. The second pole contributes additional phaseshift but the integrator is still stable because β is one at theunity-gain frequency. FIG. 7b shows A versus 1/β for an integrator witha unity gain feedback amplifier, and where the main and feedbackamplifiers are two identical two-pole amplifiers. Additional phase shiftcaused by the second poles of both op-amps degrades the phase margin ofthe integrator, and it can become unstable when the gain of the tuningamplifier is increased, as discussed above.

FIG. 7c is a graph of A vs. 1/β for a non-inverting integrator accordingto the present invention, as shown in FIG. 3. The feedback resistors, R₁and R₂, combined with the input capacitance of the feedback (i.e.,tuning) amplifier produce a pole which may cause instability.Accordingly, the resistances of the feedback amplifier must be chosen sothat the effect of this pole is outside the unity gain bandwidth. Thiscan be achieved by using small resistors and minimizing the size of theinput stage of the feedback amplifier.

It should be noted, however, that using small resistances also increasesthe power requirements for the tuning amplifier. If the resistances aretoo small, the tuning amplifier will need to drive so much power that itcan no longer be made simple in comparison to the main filter amplifier,thus making it more difficult to design the tuning filter to have abandwidth greater than that of the main amplifier.

When the tuning amplifier 26 is used to multiply the effectivecapacitance, the bandwidth of the tuning amplifier must be increasedbeyond that required for an amplifier used only for tuning. As will beapparent to those of skill in the art, the greater the gain of thetuning amplifier 26, the greater its bandwidth must be relative to themain amplifier 20 to keep the circuit stable.

Finally, a further advantage of the capacitor-tuner integrator accordingto the present invention is that the tuning amplifier improves thequality factor, Q, in a manner similar to that seen in phase-leadintegrators. The quality factor for an integrator according to thepresent invention is given by: ##EQU3## where wt₂ and wt₁ correspond tothe unity gain bandwidth of the main and tuning amplifiers respectively.See, e.g, Schaumann, Ghausi, and Laker, "Design of Analog Filters," Chp.4, Prentice Hall, Englewood Cliffs, 1990.

From Equation 3, it can be seen that Q will approach infinity if theunity gain bandwidth of the two amplifiers is perfectly matched. Since,according to the present invention, the bandwidth of the tuningamplifier is larger than that of the main amplifier so that the circuitis stable, the amplifiers cannot be identical. However, if the bandwidthof the tuning amplifier is large compared to that of the main amplifier,Equation 3 reduces to Q=wt₂ /w₁ the equation for a conventionalintegrator.

It should be noted that Equation 3 is derived for the case of a unitygain feedback amplifier, which corresponds to the case when the tuningamplifier 26 is used only to tune the filter (i.e., has a gain in therange of 0.5 to 1.5) and not as a tunable capacitor multiplier. However,a similar analysis may be performed for this situation, as will beapparent to those skilled in the art.

I claim:
 1. A tunable integrator circuit comprising:a main amplifier; aresistor connected to an input of said main amplifier; a tuningamplifier having a variable gain and being driven by an output of saidmain amplifier, said tuning amplifier having a bandwidth which isgreater than a bandwidth of said main amplifier; and a capacitorconnected between the output of said tuning amplifier and the input ofsaid main amplifier; wherein said tuning amplifier comprises: anoperational amplifier having an inverted and a non-inverted output andan inverting and a non-inverting input; a first input resistor connectedto said inverting input; a second input resistor connected to saidnon-inverting input; a first output resistor connected to said invertedoutput; a second output resistor connected to said non-inverted output;a first MOS transistor connected between said first output resistor andsaid inverting input; a second MOS transistor connected between saidfirst output resistor and said non-inverting input; a third MOStransistor connected between said second output resistor and saidinverting input; and a fourth MOS transistor connected between saidsecond output resistor and said non-inverting input; wherein the gate ofsaid first transistor is connected to the gate of said fourthtransistor; the gate of said second transistor is connected to the gateof said third transistor; and the gain of said tuning amplifier isdetermined by a reference voltage applied between said connected firstand fourth transistor gates and said connected second and thirdtransistor gates.
 2. The circuit of claim 1, wherein the gain of saidtuning amplifier is variable between about 0.5 and 1.5.
 3. The circuitof claim 1, wherein said capacitor comprises a capacitor array.
 4. Atunable biquad integrator circuit comprising:a first main amplifierhaving inverted and a non-inverted outputs and inverting and anon-inverting inputs; a first resistor connected between the invertedoutput of said first main amplifier and the inverting input of saidfirst main amplifier; a second resistor connected between thenon-inverted output of said first main amplifier and the non-invertinginput of said first main amplifier; a second main amplifier havinginverted and non-inverted outputs and inverting and non-invertinginputs; a third resistor connected between the inverted output of saidfirst main amplifier and the non-inverting input of said second mainamplifier; a fourth resistor connected between the non-inverted outputof said first main amplifier and the inverting input of said second mainamplifier; a fifth resistor connected between the inverting output ofsaid second main amplifier and the inverting input of said first mainamplifier; a sixth resistor connected between the non-inverting outputof said second main amplifier and the non-inverting input of said firstmain amplifier; a first variable gain tuning amplifier having invertedand non-inverted outputs and an inverting input being driven by theinverted output of said first main amplifier and a non-inverting inputbeing driven by the non-inverted output of said first main amplifier; afirst capacitor connected between the inverted output of said firsttuning amplifier and the non-inverting input of said first mainamplifier; a second capacitor connected between the non-inverted outputof said first tuning amplifier and the inverting input of said firstmain amplifier; a second variable gain tuning amplifier having invertedand a non-inverted outputs and an inverting input being driven by theinverted output of said second main amplifier and a non-inverting inputbeing driven by the non-inverted output of said second main amplifier; athird capacitor connected between the inverted output of said secondtuning amplifier and the non-inverting input of said second mainamplifier; and a fourth capacitor connected between the non-invertedoutput of said second tuning amplifier and the inverting input of saidsecond main amplifier.